document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=626744>Question 626744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, please help me solve:\r<BR>\n" );
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document.write( "A first line in the xy-plane is given by y= 2x-1 and a second line is given by <BR>\n" );
document.write( "y= x+1.<BR>\n" );
document.write( "a) find the coordinates of the point P of intersection of these two lines.<BR>\n" );
document.write( "b) find the distance from the origin (0,0) to the point P.\r<BR>\n" );
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document.write( "Thank you so much!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #394431 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10556)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=394431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Hello, please help me solve:\r<BR>\n" );
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document.write( "A first line in the xy-plane is given by y= 2x-1 and a second line is given by <BR>\n" );
document.write( "y= x+1.<BR>\n" );
document.write( "a) find the coordinates of the point P of intersection of these two lines.<BR>\n" );
document.write( "b) find the distance from the origin (0,0) to the point P.\r<BR>\n" );
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document.write( "Thank you so much! \r<BR>\n" );
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document.write( "Since the equations are non-parallel (different slopes) they will intersect each other. We can therefore say that since y = 2x - 1, and y = x + 1, then:\r<BR>\n" );
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document.write( "2x - 1 = x + 1<BR>\n" );
document.write( "2x - x = 1 + 1<BR>\n" );
document.write( "x = 2\r<BR>\n" );
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document.write( "y = 2(2) - 1 ----- Substituting 2 for x in equation<BR>\n" );
document.write( "y = 4 - 1<BR>\n" );
document.write( "y = 3\r<BR>\n" );
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document.write( "Since x = 2, and y = 3, then point of intersection of both lines, or P = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%282%29 ALIGN=MIDDLE  ALT=\"highlight_green%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%283%29 ALIGN=MIDDLE  ALT=\"highlight_green%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Drawing a diagram, you will see that the distance from the origin, (0, 0) to P (point of intersection) is represented as the hypotenuse of a right-triangle, with one leg measuring 2 units (on the x-axis), and another leg measuring 3 units (vertical and parallel to the y-axis), on the xy-plane. \r<BR>\n" );
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document.write( "With H being the length of the hypotenuse, we have: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2+=+2%5E2+%2B+3%5E2 ALIGN=MIDDLE  ALT=\"H%5E2+=+2%5E2+%2B+3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2+=+4+%2B+9 ALIGN=MIDDLE  ALT=\"H%5E2+=+4+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2+=+13 ALIGN=MIDDLE  ALT=\"H%5E2+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+sqrt%2813%29 ALIGN=MIDDLE  ALT=\"H+=+sqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The distance from the origin (0, 0) to P (point of intersection), or coordinate point (2, 3) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28sqrt%2813%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28sqrt%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at  MathMadEzy@aol.com </SPAN>\n" );
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